Field of the Invention
The present invention uses a technology used in so-called digital holographic imaging, and in a realistic image forming optical system, this invention relates to a method of acquiring an optical phase and the distribution of the optical phase on, for example, an exit pupil plane of the optical system that is useful when the optical system is evaluated. The realistic image forming optical system is configured by, for example, coaxially arranging one or more image forming optical elements such as a lens having a refractive surface of a concave surface or a convex surface, a lens (GRIN lens) achieved by the fact that a refractive medium has a specific refractive index distribution, and a mirror having a reflective surface of a concave surface or a convex surface. In this method, extant input image points located at prescribed extant input image spatial coordinates are actually input to obtain interference image data with respect to each extant input image point; however, while the number of the extant input image points is suppressed within a range where the interference image data can be economically obtained, in addition to aberration as designed, error in profile of a refractive surface or a reflective surface of each image forming optical element and internal presence of defects such as eccentricity, surface distance error, and assembly error such as tilt are included. Further, in this method, diffractive optical image forming simulation with respect to an arbitrary input image pattern is performed, for example, or OTF and Zernike expanding coefficients are calculated, whereby the optical system is evaluated.
By using the present method, when an image of an unrealistic arbitrary virtual input pattern is formed by a realistic optical system, an output pattern, a resolution, and so on can be confirmed through simulation. Therefore, this method is applicable to inspection of an image forming performance of a realistic optical system, for example.
Description of the Related Art
By virtue of the development of pixel densification in a recent imaging element such as CCD and MOS image sensor, the increase in the capacity of a storage of a calculator, and speeding up of calculation, a digital holographic imaging technology can be relatively easily applied.
The digital holographic imaging technology will be described here. In the original optical holography, a photographic plate on which a hologram interference fringe is recorded is developed, and an image of a stereoscopic image reconstructed by being illuminated with light having the same condition as that of reference light irradiated during recording is formed. In the digital holographic imaging technology, a hologram interference fringe is obtained as digital data by filming in use of an imaging element instead of the photographic plate. An optical phenomenon that may occur when the hologram interference fringe is irradiated with light is simulated using a computer, whereby a stereoscopic image is reconstructed.
As the contents of the simulation, a bright and dark pattern of an imaged hologram interference fringe is regarded as an optical filter whose light transmittance changes depending on a position on a plane. Assuming a case where this is irradiated with light, the transmitted light, that is, light subjected to amplitude modulation while depending on the position on the plane propagates in a space as wave motion, and light electric field distribution formed on a virtual plane defined at an arbitrary rear position is reconstructed including phase information.
Accordingly, when the position of the virtual plane is taken on an output image plane of an optical system, the real image or virtual image can be reconstructed and confirmed.
The light propagation is a diffraction phenomenon called a Fresnel diffraction or Fraunhofer diffraction according to propagation distance conditions, and although the simulation is performed by diffractive optical light propagation simulation in which a possible approximation is applied to the formula called Kirchhoff-Huygens diffraction integral formula, the simulation is usually formulated such that light wave motion is a light electric field of complex numbers (a vibration component depending on the time is omitted).
Note that, including history, a method of digital holographic imaging is described in WO2008/123408.
When evaluation of an image forming performance of a realistic image forming optical system is desired, in the prior art, a wide variety of test patterns have been input to evaluate the output image.
However, in order to evaluate an optical system from various viewpoints, it is expected that, instead of inputting many test patterns, light electric field distribution output when typical point images are input is previously acquired including phase information, and flexible evaluation is achieved by performing simulation with respect to a wide variety of conditions, including a virtual input pattern as a test pattern to be input. Thus, the digital holographic imaging technology can be applied thereto.
As an apparatus which evaluates an optical system with the use of the digital holographic imaging technology, JP-A-2003-098040 describes an evaluation apparatus which numerically reproduces a light wave passing through a tested optical system (lens) and obtaining light amount distribution of the light wave passing through the tested optical system on a plane substantially perpendicular to the optical axis.
It is further described that a beam diameter of the reproduced light wave and distribution profile are examined
It is further described that ray tracing simulation is performed using surface form data of lens and internal refractive index distribution data of the lens together, thus obtaining equiphase plane data.
It is further described that the influence of birefringence inside the lens on a passage optical wavefront of the lens is examined based on a difference between the equiphase plane data, obtained by the ray tracing simulation based on the surface form data of the lens and the internal refractive index distribution data of the lens, and equiphase plane data of an optical wavefront reproduced based on hologram image data.
It is further described that the light wave passing through the tested optical system is numerically reproduced, and in an optical axis direction of the light wave passing through the tested optical system, light amount distribution of the light wave passing through the tested optical system on a plane substantially perpendicular to the optical axis is obtained.
It is further described that the overall influence of internal non-uniformity of each lens used in a scanning optical system on the light wave passing through the tested optical system is examined
It is furthermore described that the overall influence of birefringence of each lens used in the optical system on the light wave passing through the tested optical system is examined
JP-W-2002-526815 describes a technique of acquiring a phase contrast image by digital holographic imaging and multiplying a phase mask function in order to correct an aberration of a magnification or demagnification optical system.
U.S. Pat. No. 7,649,160 describes a technique of automatically or semi-automatically correcting defects of an image due to tilt of an optical axis for off-axis, aberration of an objective lens or the like, error in adjustment of an optical system, defocusing, hand movement, and so on with the use of digital wave front operation of digital holographic imaging.
As described above, the above prior arts merely evaluate physical characteristics inside an optical system, light quantity distribution of an output light flux, and so on with the use of the digital holographic imaging technology or correct defects of a taken image due to aberration of the optical system and defects of photographing conditions and thus cannot confirm and evaluate an output pattern, a resolution, and so on through simulation when an image of an arbitrary virtual input pattern is formed.